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Let's say you want to divide x squared plus 3x minus 40 by x minus 5. First step is we take this x minus 5 and put it outside the long division symbol. Inside the long division, we put x squared plus 3x minus 40. Now the first question we've got to ask ourselves is what do we need to multiply by x minus 5 to give us an x squared in return. The answer is we need an x. We work out now what x multiplied by x minus 5 gives us.and the answer is x squared minus 5x. We then subtract this from our original polynomial.which gives us x squared minus x squared.zero.plus 3x minus 5x, which is plus 8x and bring this minus 40 all the way down. And then we start again from this step. We ask ourselves, what is it we need to multiply by.x minus 5 to give us 8x. The answer is we need a plus 8. Now we work out what 8 multiplied by x minus 5 is going to give us.and the answer is 8x minus 40. and once again, we subtract this from the line above, which give us.8x minus 8x.zero, and minus 40 minu 40.which is also 0. It shos us that we have completely divided x squared plus 3x minus 40.showing us that the answer to this is in fact what we've written here.x plus 8. And that is how to divide polynomials.
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